Addition Rules for Probability
CHAPTER 4.2
A person is female
A person is Republican
A person is both female and a Republican
A person is a Democrat
A person is an Independent
CONSIDER THE DIFFERENCE BETWEEN:
Two events are mutually exclusive events if they cannot occur at the same time
For example, the events of getting a 4 and getting a 6 when a single card is drawn from a deck are mutually exclusive events.
The events of getting a 4 and getting a heart on a single draw are not mutually exclusive
MUTUALLY EXCLUSIVE
1. Getting an odd number and getting an even number.
2. Getting a 3 and getting an odd number
3. Getting an odd number and getting a number less than 4
4. Getting a number greater than 4 and getting a number less than 4
DETERMINE WHICH EVENTS ARE MUTUALLY EXCLUSIVE AND WHICH ARE NOT WHEN A SINGLE DIE IS
ROLLED.
1. Getting a 7 and getting a jack
2. Getting a club and getting a king
3. Getting a face card and getting an ace
4. Getting a face card and getting a spade
DETERMINE WHICH EVENTS ARE MUTUALLY EXCLUSIVE AND WHICH ARE NOT WHEN A SINGLE CARD IS
DRAWN
When two events A and B are mutually exclusive, the probability that A or B will occur is
P(A or B) = P(A) + P(B)
ADDITION RULE FOR MUTUALLY EXCLUSIVE EVENTS
A city has 9 coffee shops: 3 Starbuck’s, 2 Caribou Coffees, and 4 Crazy Mocho Coffees. If a person selects one shop at random to buy a cup of coffee, find the probability that it is either a Starbuck’s or Crazy Mocho Coffees.
COFFEE SHOP SELECTION
The corporate research and development centers for three local companies have the following number of employees.
U.S. Steel 110Alcoa 750Bayer Material Science 250
If a research employee is selected at random, find the probability that the employee is employed by U.S. Steel or Alcoa.
RESEARCH AND DEVELOPMENT EMPLOYEES
If A and B are not mutually exclusive, then
P(A or B) = P(A) + P(B) – P(A and B)
ADDITION RULE FOR EVENTS THAT ARE NOT MUTUALLY EXCLUSIVE
A single card is drawn at random from an ordinary deck of cards. Find the probability that it is either an ace or a black card.
DRAWING A CARD
In a hospital unit, there are 8 nurses and 5 physicians; 7 nurses and 3 physicians are females. If a staff person is selected at random, find the probability that the subject is a nurse or a male.
SELECTING A MEDICAL STAFF PERSON
On New Year’s Eve, the probability of a person driving while intoxicated is 0.32, the probability of a person having a driving accident is 0.09, and the probability of person having a driving accident while intoxicated is 0.06. What is the probability of a person driving while intoxicated or having a driving accident?
DRIVING WHILE INTOXICATED
Pg. 211-212 Applying the concepts:
TRY IT!
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